My animation has no keyframes but still moves?
You have 2 armatures, Track Controller (with only one bone, on the left of the machine), and Armature, which is all the machine bones.

Your Dopesheet is in Action Editor mode, it will only display the keyframes relative to the selected armature. 

When we open the file, Track Controller is selected, and as it has no action, no keyframes are displayed.

On the contrary, we can see that Armature is animated. It's normal because an action has been assigned to it, and if we select this armature, all the keyframes of this action will be displayed on the Dopesheet.

If you want to close the action playing for a selected object, press the X button on the right of the action name. It won't be played anymore by the armature but it will still be selectable in the dropdown menu if you want it back.



When you close your file, every action will be saved as long as it has at least one user (one object or armature using it) or if you've assigned it a fake user (press the F button on the right of the action name if you want to give an action a fake user). Fake user is a way to make sure that the action you've created will be saved even if it doesn't have any user yet.

About le leap to the side: your bones come back to their rest pose as soon as you come back to Edit mode. If you select all these bones in Pose mode and press altG they will combe back to the same pose.